Computational Intelligence and Neuroscience / 2019 / Article / Tab 7

Research Article

An Opposition-Based Evolutionary Algorithm for Many-Objective Optimization with Adaptive Clustering Mechanism

Table 7

The statistical results (mean and standard deviation) of the IGD values obtained by RVEA, NSGA-III, SPEAR, MOEA/DD, Two_Arch2, MOEA/DVA, and OBEA on DTLZ test suits. The best results are italicized.

ProblemMRVEANSGA-IIISPEARMOEA/DDTwo_Arch2MOEA/DVAOBEA

DTLZ134.997e − 1 (3.35e − 1) −2.608e − 1 (2.03e − 1) −1.100e − 1 (1.30e − 1) −4.459e − 1 (2.52e − 1) −4.650e − 2 (2.52e − 2) −3.599e − 1 (2.57e − 1) −1.121e − 2 (5.13e − 4)
51.102e + 0 (5.51e − 1) −1.511e + 0 (5.80e − 1) −1.416e − 1 (7.28e − 2) −1.030e + 0 (4.11e − 1) −6.561e − 2 (6.73e − 3) −5.957e − 2 (2.36e − 3) −5.101e − 2 (4.27e − 4)
86.312e − 1 (3.18e − 1) −1.960e + 0 (6.81e − 1) −2.331e − 1 (6.85e − 2) −5.884e − 1 (2.74e − 1) −1.190e − 1 (1.61e − 2) −1.034e − 1 (1.24e − 3) −8.202e − 2 (2.51e − 3)
109.947e − 1 (3.36e − 1) −3.182e + 0 (1.57e + 0) −5.290e − 1 (2.83e − 1) −1.057e + 0 (6.06e − 1) −1.453e − 1 (2.12e − 2) −1.119e − 1 (7.27e − 4) =1.312e − 1 (3.09e − 3)
153.456e − 1 (1.19e − 1) =1.189e + 0 (5.61e − 1) −7.744e + 0 (4.56e + 0) −3.937e − 1 (2.88e − 1) =2.518e − 1 (1.01e − 1) −1.332e − 1 (1.88e − 3) =1.214e − 1 (3.01e − 3)

DTLZ235.569e − 2 (4.96e − 4) −5.495e − 2 (1.42e − 4) −7.230e − 2 (2.57e − 3) −5.541e − 2 (4.55e − 4) =3.644e − 2 (6.21e − 4) +5.164e − 2 (9.58e − 4) =5.479e − 2 (9.14e − 5)
51.759e − 1 (2.14e − 3) −1.859e − 1 (3.63e − 3) −2.154e − 1 (1.13e − 2) −1.725e − 1 (1.76e − 3) =2.106e − 1 (1.61e − 3) −2.044e − 1 (2.70e − 3) −1.696e − 1 (9.83e − 4)
83.289e − 1 (1.99e − 3) +4.330e − 1 (1.00e − 1) −4.297e − 1 (4.62e − 2) −3.285e − 1 (2.60e − 3) +3.512e − 1 (2.88e − 3) =3.167e − 1 (1.98e − 3) =3.335e − 1 (2.51e − 3)
104.239e − 1 (4.74e − 3) =6.047e − 1 (8.69e − 2) −8.016e − 1 (4.78e − 2) −4.233e − 1 (5.31e − 3) =4.788e − 1 (6.39e − 3) −4.689e − 1 (2.62e − 3) −4.215e − 1 (3.95e − 3)
155.968e − 1 (1.77e − 2) =7.367e − 1 (5.21e − 2) −7.433e − 1 (4.78e − 2) −6.068e − 1 (2.31e − 2) −6.179e − 1 (6.59e − 3) −5.086e − 1 (2.58e − 3) +5.885e − 1 (5.97e − 3)

DTLZ331.546e + 1 (4.20e + 0) −1.038e + 1 (3.51e + 0) −8.519e − 1 (7.73e − 1) =1.794e + 1 (5.90e + 0) −2.827e + 0 (1.13e + 0) −5.682e + 1 (1.18e + 1) −5.494e − 1 (3.21e − 2)
54.328e + 1 (1.02e + 1) −5.736e + 1 (1.20e + 1) −1.165e + 1 (6.04e + 0) −5.004e + 1 (1.05e + 1) −1.779e + 0 (1.23e + 0) −4.175e − 1 (2.50e − 1) −1.782e − 1 (2.51e − 3)
82.744e + 1 (9.59e + 0) −7.911e + 1 (2.93e + 1) −4.192e + 0 (2.77e + 0) −3.024e + 1 (8.72e + 0) −7.705e + 0 (2.79e + 0) −2.086e + 0 (1.77e + 0) −8.911e − 1 (8.01e − 1)
104.608e + 1 (1.38e + 1) −1.403e + 2 (2.52e + 1) −3.490e + 1 (1.11e + 1) −5.597e + 0 (1.09e + 1) −1.484e + 1 (2.95e + 0) −2.567e + 0 (9.06e − 1) =1.197e + 0 (4.32e − 1)
151.996e + 1 (7.94e + 0) −1.360e + 2 (5.17e + 1) −1.968e + 2 (6.42e + 1) −2.072e + 0 (9.46e + 0) −4.698e + 1 (9.88e + 0) −2.117e + 0 (1.20e + 0) −1.569e + 0 (4.91e − 1)

DTLZ435.607e − 2 (6.32e − 4) +1.686e − 1 (2.09e − 1) +8.126e − 2 (1.65e − 2) +5.548e − 2 (3.79e − 4) +3.623e − 2 (4.36e − 4) +5.949e − 1 (1.81e − 3) −1.851e − 1 (2.20e − 1)
51.794e − 1 (3.97e − 3) −1.997e − 1 (4.50e − 2) −4.009e − 1 (2.69e − 2) −1.780e − 1 (4.35e − 3) =1.663e − 1 (2.42e − 3) =1.558e − 1 (6.58e − 4) =1.770e − 1 (1.44e − 2)
83.489e − 1 (1.15e − 2) =4.614e − 1 (9.89e − 2) −5.482e − 1 (3.18e − 2) −3.539e − 1 (2.72e − 2) =3.510e − 1 (3.34e − 3) =3.192e − 1 (3.70e − 4) =3.478e − 1 (1.95e − 3)
104.640e − 1 (4.80e − 3) =5.677e − 1 (4.65e − 2) −6.921e − 1 (2.76e − 2) −4.763e − 1 (1.28e − 2) =4.285e − 1 (3.09e − 3) =4.713e − 1 (2.57e − 2) −4.631e − 1 (3.80e − 3)
156.366e − 1 (9.63e − 3) =8.185e − 1 (6.48e − 2) −8.189e − 1 (4.44e − 2) −6.413e − 1 (1.21e − 2) −5.670e − 1 (1.11e − 2) =5.285e − 1 (1.30e − 2) +6.306e − 1 (1.38e − 3)

DTLZ731.934e − 1 (3.76e − 2) −1.204e − 1 (7.52e − 2) =2.814e − 1 (7.45e − 2) −5.516e − 1 (2.48e − 1) =4.901e − 2 (3.96e − 3) +4.045e − 2 (1.08e − 3) +5.452e − 2 (3.12e − 3)
58.014e − 1 (1.00e − 1) −8.126e − 1 (1.19e − 1) −1.460e + 0 (4.28e − 1) −2.045e + 0 (4.82e − 1) +2.046e − 1 (9.47e − 3) +3.023e − 1 (2.62e − 2) +4.141e − 1 (5.13e − 2)
81.621e + 0 (6.52e − 1) =4.793e + 0 (7.44e − 1) −5.423e + 0 (1.09e + 0) −1.574e + 0 (4.65e − 1) −6.024e − 1 (1.86e − 2) +1.282e + 0 (2.53e − 1) −9.146e − 1 (3.31e − 2)
103.657e + 0 (1.87e + 0) =1.325e + 1 (1.41e + 0) −1.656e + 1 (2.73e + 0) −1.530e + 0 (1.13e − 1) =1.614e + 0 (4.31e − 2) =2.094e + 0 (2.68e − 1) =1.452e + 0 (6.76e − 1)
155.228e + 0 (2.67e + 0) =1.779e + 1 (2.38e + 0) −1.896e + 1 (1.78e + 0) −3.201e + 0 (1.22e − 1) −1.078e + 1 (7.13e − 1) −3.241e + 0 (3.75e − 1) −1.953e + 0 (3.87e − 1)

2/14/91/23/12/22/13/13/95/14/64/15/6